Martinez was hotly tipped to take the reins at Anfield earlier in the summer, but he has revealed he was convinced to stay due to chairman Dave Whelan's ambition.
"I stayed because my chairman is unique," The Mirror quotes Martinez as saying. "This summer, we sat down together. He had thought about the future of the club, I'd done the same.
"He knew that I had spoken with other clubs. But he is so persuasive... I extended my contract for three years.
"He wants to take the club to the next level. I know it will be difficult, but it excites me a lot."
Martinez has been manager of Wigan since June 2009.